{"id":{"repo_id":"lsu-thes","oai_identifier":"oai:repository.lsu.edu:gradschool_dissertations-1789"},"canonical_url":"https://search.dev.ndltd.org/etd/lsu-thes/oai:repository.lsu.edu:gradschool_dissertations-1789","repository":{"repo_id":"lsu-thes","name":"Lousiana State University","base_url":"https://repository.lsu.edu/do/oai/"},"display":{"title":"Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains.","abstract":"This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function space which yields such sharp existence results. Finally in Chapter 6, we prove existence of very weak solutions to quasilinear equations below the natural exponent with measure data on the right.","abstract_html":"This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function space which yields such sharp existence results. Finally in Chapter 6, we prove existence of very weak solutions to quasilinear equations below the natural exponent with measure data on the right.","abstract_has_math":false,"creators":["Adimurthi, Karthik"],"institution":"Mathematics","degree_name":"Doctor of Philosophy (PhD)","degree_level":"Dissertation","degree_discipline":"Applied Mathematics","degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2016,"date_issued":"2016-01-01T08:00:00Z","date_published":"2016-01-01T08:00:00Z","updated_at":"2026-07-24T02:58:17Z","subjects":["weighted estimates","p-Laplacian","existence of weak solution"],"languages":[],"rights":["unrestricted","Release the entire work immediately for access worldwide."],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04062016-020401","https://repository.lsu.edu/gradschool_dissertations/790"],"render_values":[{"text":"etd-04062016-020401","href":null,"code":true},{"text":"https://repository.lsu.edu/gradschool_dissertations/790","href":"https://repository.lsu.edu/gradschool_dissertations/790","code":true}]}]},"links":{"outbound_url":"https://doi.org/10.31390/gradschool_dissertations.790","outbound_label":"DOI","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Adimurthi, Karthik"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2016-03-29"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2022-05-12T23:10:00Z"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Applied Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy (PhD)"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Mathematics"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["weighted estimates","p-Laplacian","existence of weak solution"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:rights","label":"Dc Rights","values":["unrestricted","Release the entire work immediately for access worldwide."]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["etd-04062016-020401","10.31390/gradschool_dissertations.790","https://repository.lsu.edu/gradschool_dissertations/790"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function space which yields such sharp existence results. Finally in Chapter 6, we prove existence of very weak solutions to quasilinear equations below the natural exponent with measure data on the right."]},{"key":"dc:title","label":"Title","values":["Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains."]}]}],"canonical_facts":{"dc:creator":["Adimurthi, Karthik"],"dc:date":["2016-03-29"],"dc:date.available":["2022-05-12T23:10:00Z"],"dc:description.abstract":["This thesis deals obtaining global a priori estimates for quasilinear elliptic equations and sharp existence results for Quasilinear equations with gradient nonlinearity on the right. The main results are contained in Chapters 3, 4, 5 and 6. In Chapters 3 and 4, we obtain global unweighted a priori estimates for very weak solutions below the natural exponent and weighted estimates at the natural exponent. The weights we consider are the well studied Muckenhoupt weights. Using the results obtained in Chapter 4, we obtain sharp existence result for quasilinear operators with gradient type nonlinearity on the right. We characterize the function space which yields such sharp existence results. Finally in Chapter 6, we prove existence of very weak solutions to quasilinear equations below the natural exponent with measure data on the right."],"dc:identifier":["etd-04062016-020401","10.31390/gradschool_dissertations.790","https://repository.lsu.edu/gradschool_dissertations/790"],"dc:rights":["unrestricted","Release the entire work immediately for access worldwide."],"dc:subject":["weighted estimates","p-Laplacian","existence of weak solution"],"dc:title":["Global a priori Estimates and Sharp Existence Results for Quasilinear Equations on Nonsmooth Domains."],"thesis:degree_discipline":["Applied Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy (PhD)"],"thesis:institution_name":["Mathematics"]},"updated_at":"2026-07-24T02:58:17Z"}